Abstract

This paper presents a study of bifurcations and synchronization {in the sense of Pecora and Carroll [Phys. Rev. Lett. 64, 821–824 (1990)]} in the Moore–Spiegel oscillator equations. Complicated patterns of period-doubling, saddle-node, and homoclinic bifurcations are found and analyzed. Synchronization is demonstrated by numerical experiment, periodic orbit expansion, and by using coordinate transformations. Synchronization via the resetting of a coordinate after a fixed interval is also successful in some cases. The Moore–Spiegel system is one of a general class of dynamical systems and synchronization is considered in this more general context.